## Controlling cascade dressing interaction of four-wave mixing image |

Optics Express, Vol. 19, Issue 14, pp. 13675-13685 (2011)

http://dx.doi.org/10.1364/OE.19.013675

Acrobat PDF (1665 KB)

### Abstract

We report our observations on enhancement and suppression of spatial four-wave mixing (FWM) images and the interplay of four coexisting FWM processes in a two-level atomic system associating with three-level atomic system as comparison. The phenomenon of spatial splitting of the FWM signal has been observed in both *x* and *y* directions. Such FWM spatial splitting is induced by the enhanced cross-Kerr nonlinearity due to atomic coherence. The intensity of the spatial FWM signal can be controlled by an additional dressing field. Studies on such controllable beam splitting can be very useful in understanding spatial soliton formation and interactions, and in applications of spatial signal processing.

© 2011 OSA

## 1. Introduction

1. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today **50**(7), 36–9999 (1997). [CrossRef]

4. H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A **80**(2), 023820 (2009). [CrossRef]

5. S. W. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. **98**(5), 053601 (2007). [CrossRef] [PubMed]

6. Y. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. **91**(6), 061113 (2007). [CrossRef]

7. M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A **60**(4), 3225–3228 (1999). [CrossRef]

8. M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A **64**(1), 013412 (2001). [CrossRef]

*et al.*[7

7. M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A **60**(4), 3225–3228 (1999). [CrossRef]

*et al.*, verified the existence of the secondarily dressed states [8

8. M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A **64**(1), 013412 (2001). [CrossRef]

9. Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A **77**(6), 063829 (2008). [CrossRef]

10. Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler-Townes splitting in high-order nonlinear processes,” Opt. Lett. **35**(20), 3420–3422 (2010). [CrossRef] [PubMed]

11. C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. **95**(4), 041103 (2009). [CrossRef]

12. G. P. Agrawal, “Induced focusing of optical beams in self-defocusing nonlinear media,” Phys. Rev. Lett. **64**(21), 2487–2490 (1990). [CrossRef] [PubMed]

13. R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud Jr, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. **88**(11), 113901 (2002). [CrossRef] [PubMed]

14. A. J. Stentz, M. Kauranen, J. J. Maki, G. P. Agrawal, and R. W. Boyd, “Induced focusing and spatial wave breaking from cross-phase modulation in a self-defocusing medium,” Opt. Lett. **17**(1), 19–21 (1992). [CrossRef] [PubMed]

15. H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. **87**(7), 073601 (2001). [CrossRef] [PubMed]

17. Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A **82**(5), 053837 (2010). [CrossRef]

16. W. Królikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. **80**(15), 3240–3243 (1998). [CrossRef]

18. P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, “Storage and retrieval of multimode transverse images in hot atomic Rubidium vapor,” Phys. Rev. Lett. **100**(12), 123903 (2008). [CrossRef] [PubMed]

19. V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science **321**(5888), 544–547 (2008). [CrossRef] [PubMed]

20. W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. L. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. **85**(7), 1424–1427 (2000). [CrossRef] [PubMed]

21. Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four- wave mixing and six-wave mixing channels,” Phys. Rev. Lett. **102**(1), 013601 (2009). [CrossRef] [PubMed]

*x*and

*y*directions of DFWM signal due to different spatially alignment of the probe and coupling beams.

## 2. Theoretical model and experimental scheme

## 3. Cascade dressing interaction

10. Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler-Townes splitting in high-order nonlinear processes,” Opt. Lett. **35**(20), 3420–3422 (2010). [CrossRef] [PubMed]

*x*-direction of the FWM signal beams induced by additional dressing laser beams is observed simultaneously as shown in Fig. 5(a) . It is observed that, the number of the splitting spots increases when the FWM intensity is suppressed. To understand these phenomena, we need to consider the cross-phase modulation (XPM) on the FWM signals. As described in our previous investigation [17

17. Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A **82**(5), 053837 (2010). [CrossRef]

*ϕ*) distribution in the laser propagating equations determines the spatial splitting of the laser beams. In theoretical calculation, we can obtain the intensity of the

17. Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A **82**(5), 053837 (2010). [CrossRef]

*ϕ*is primarily determined by

*ϕ*is decreased, and therefore the splitting is weakened correspondingly, as shown in Fig. 5(a), where the enhancement condition is located at

*y*-direction spatial splitting images of the DFWM signal

*y-z*plane with an angle

*θ*(

*θ*is far less than the angle of

*x-z*plane,

*Λ*is big enough for observing the splitting caused by the induced grating. Furthermore when

*y*-direction due to the phase matching condition. As a result, the splitting of

*x*-direction due to the nonlinear cross-Kerr effect from

*Λ*remains nearly the same for the changeless

*θ*and

*y*-direction. So we can easily obtain the splitting in

*y*-direction. Moreover, in the enhanced position, the profile of the FWM signal become larger, and more split parts induced by the grating can be obtained. Here, Figs. 5(b1)-5(b3) show the experimental spots corresponding to the curves in Figs. 4(c1)-4(c3). However, the effects of suppression and enhancement of the DFWM signal

*y*-direction. So the dressing effect on

*x*direction spatial splitting of DFWM signal

## 4. Conclusion

## Acknowledgments

## References and links

1. | S. E. Harris, “Electromagnetically induced transparency,” Phys. Today |

2. | P. R. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. S. Shahriar, and P. Kumar, “Efficient low-intensity optical phase conjugation based on coherent population trapping in sodium,” Opt. Lett. |

3. | B. Lü, W. H. Burkett, and M. Xiao, “Nondegenerate four-wave mixing in a double-Lambda system under the influence of coherent population trapping,” Opt. Lett. |

4. | H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A |

5. | S. W. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. |

6. | Y. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. |

7. | M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A |

8. | M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A |

9. | Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A |

10. | Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler-Townes splitting in high-order nonlinear processes,” Opt. Lett. |

11. | C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. |

12. | G. P. Agrawal, “Induced focusing of optical beams in self-defocusing nonlinear media,” Phys. Rev. Lett. |

13. | R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud Jr, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. |

14. | A. J. Stentz, M. Kauranen, J. J. Maki, G. P. Agrawal, and R. W. Boyd, “Induced focusing and spatial wave breaking from cross-phase modulation in a self-defocusing medium,” Opt. Lett. |

15. | H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. |

16. | W. Królikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. |

17. | Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A |

18. | P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, “Storage and retrieval of multimode transverse images in hot atomic Rubidium vapor,” Phys. Rev. Lett. |

19. | V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science |

20. | W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. L. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. |

21. | Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four- wave mixing and six-wave mixing channels,” Phys. Rev. Lett. |

**OCIS Codes**

(190.3270) Nonlinear optics : Kerr effect

(190.4180) Nonlinear optics : Multiphoton processes

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(270.1670) Quantum optics : Coherent optical effects

(300.2570) Spectroscopy : Four-wave mixing

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: April 11, 2011

Revised Manuscript: May 21, 2011

Manuscript Accepted: June 19, 2011

Published: June 30, 2011

**Citation**

Changbiao Li, Yanpeng Zhang, Huaibin Zheng, Zhiguo Wang, Haixia Chen, Suling Sang, Ruyi Zhang, Zhenkun Wu, Liang Li, and Peiying Li, "Controlling cascade dressing interaction of four-wave mixing image," Opt. Express **19**, 13675-13685 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-14-13675

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### References

- S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–9999 (1997). [CrossRef]
- P. R. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. S. Shahriar, and P. Kumar, “Efficient low-intensity optical phase conjugation based on coherent population trapping in sodium,” Opt. Lett. 20(9), 982–984 (1995). [CrossRef] [PubMed]
- B. Lü, W. H. Burkett, and M. Xiao, “Nondegenerate four-wave mixing in a double-Lambda system under the influence of coherent population trapping,” Opt. Lett. 23(10), 804–806 (1998). [CrossRef] [PubMed]
- H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009). [CrossRef]
- S. W. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98(5), 053601 (2007). [CrossRef] [PubMed]
- Y. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91(6), 061113 (2007). [CrossRef]
- M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60(4), 3225–3228 (1999). [CrossRef]
- M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A 64(1), 013412 (2001). [CrossRef]
- Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008). [CrossRef]
- Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler-Townes splitting in high-order nonlinear processes,” Opt. Lett. 35(20), 3420–3422 (2010). [CrossRef] [PubMed]
- C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95(4), 041103 (2009). [CrossRef]
- G. P. Agrawal, “Induced focusing of optical beams in self-defocusing nonlinear media,” Phys. Rev. Lett. 64(21), 2487–2490 (1990). [CrossRef] [PubMed]
- R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002). [CrossRef] [PubMed]
- A. J. Stentz, M. Kauranen, J. J. Maki, G. P. Agrawal, and R. W. Boyd, “Induced focusing and spatial wave breaking from cross-phase modulation in a self-defocusing medium,” Opt. Lett. 17(1), 19–21 (1992). [CrossRef] [PubMed]
- H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001). [CrossRef] [PubMed]
- W. Królikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80(15), 3240–3243 (1998). [CrossRef]
- Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82(5), 053837 (2010). [CrossRef]
- P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, “Storage and retrieval of multimode transverse images in hot atomic Rubidium vapor,” Phys. Rev. Lett. 100(12), 123903 (2008). [CrossRef] [PubMed]
- V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008). [CrossRef] [PubMed]
- W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. L. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85(7), 1424–1427 (2000). [CrossRef] [PubMed]
- Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four- wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009). [CrossRef] [PubMed]

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